-7 2/3 + (-5 1/2) + 8 2/4 =
In order to add these mixed fractions together, we first need to convert them to improper fractions.
-7 2/3 = (-7 * 3 + 2) / 3 = (-21 + 2) / 3 = -19/3
-5 1/2 = (-5 * 2 + 1) / 2 = (-10 + 1) / 2 = -9/2
8 2/4 = (8 * 4 + 2) / 4 = (32 + 2) / 4 = 34/4 = 17/2
Now we can add the fractions:
-19/3 + -9/2 + 17/2
To add fractions with different denominators, we need to find a common denominator. In this case, the least common multiple of 3 and 2 is 6.
-19/3 * 2/2 = -38/6
-9/2 * 3/3 = -27/6
Now we can add the fractions:
-38/6 + (-27/6) + 17/2
Combining the numerators:
(-38 - 27 + 51) / 6
Simplifying the numerator:
(-65 + 51) / 6 = -14/6 = -7/3
Therefore, -7 2/3 + (-5 1/2) + 8 2/4 is equal to -7/3
To add the given numbers, we need to convert all mixed numbers to improper fractions first.
-7 2/3 can be rewritten as -21/3 + 2/3
-5 1/2 can be rewritten as -10/2 + 1/2
8 2/4 can be rewritten as 8 + 2/4
Simplifying, we have:
-7 2/3 = -21/3 + 2/3 = -19/3
-5 1/2 = -10/2 + 1/2 = -9/2
8 2/4 = 8 + 2/4 = 8 + 1/2 = 16/2 + 1/2 = 17/2
Now we can add these fractions:
-19/3 + (-9/2) + 17/2
To add these fractions, we need to find a common denominator. The least common multiple (LCM) of 3 and 2 is 6.
Converting the fractions to have a denominator of 6:
-19/3 = -38/6
-9/2 = -27/6
17/2 = 51/6
Now we can add these fractions:
-38/6 + (-27/6) + 51/6
Adding the numerators, we get:
-38 - 27 + 51 = -14
So, -7 2/3 + (-5 1/2) + 8 2/4 = -14.